This invention relates to nuclear magnetic resonance (NMR) imaging methods and apparatus and more particularly to a method of producing separate images of different chemical species using such imaging methods.
In an NMR imaging sequence, a uniform magnetic field B.sub.O is applied to an imaged object along the z axis of a Cartesian coordinate system, the origin of which is within the imaged object. The effect of the magnetic field B.sub.O is to align the object's nuclear spins along the z axis. In response to RF pulses of the proper frequency oriented within the x-y plane, the nuclei resonate at their Larmor frequencies according to the following equation: EQU .omega.=.gamma.B.sub.O ( 1)
where .omega. is the Larmor frequency, and .gamma. is the gyromagnetic ratio which is a property of the particular nucleus. Water, because of its relative abundance in biological tissue and the properties of its proton nuclei, is of principle concern in such imaging. The value of the gyromagnetic ratio .gamma. for protons in water is 4.26 kHz/Gauss and therefore in a 1.5 Tesla polarizing magnetic field B.sub.O, the resonant or Larmor frequency of water protons is approximately 63.9 MHz.
Materials other than water, principally fat, are also to be found in biological tissue and have different gyromagnetic ratios. The Larmor frequency of protons in fat is approximately 203 Hz. higher than that of protons in water in a 1.5 Tesla polarizing magnetic field B.sub.O. The difference between the Larmor frequencies of such different isotopes or species of the same nucleus, viz., protons, is termed chemical shift, reflecting the differing chemical environments of the two species.
In the well known slice selective RF pulse sequence, a z axis magnetic field gradient G.sub.z is applied at the time of the RF pulse so that only the nuclei in a slice through the object in an x-y plane are excited into resonance. After the excitation of the nuclei, magnetic field gradients are applied along the x and y axes and an NMR signal is acquired. The gradient along the x axis, G.sub.x, causes the nuclei to precess at different resonant frequencies depending on their position along the x axis; that is, G.sub.x spatially encodes the precessing nuclei by frequency. Similarly, the y axis gradient, G.sub.y, is incremented through a series of values and encodes y position into the rate of change of phase as a function of G.sub.y gradient amplitude, a process typically referred to as phase encoding. From this data set an image may be derived according to well known reconstruction techniques. A general description of one such image reconstruction technique based on the Fourier transform is contained in the book "Magnetic Resonance Imaging, Principles and Applications" by D. N. Kean and M. A. Smith. Images in other orientations can be generated by rotation of the gradient directions, as is well known in the art.
Often it is desired to "decompose" the NMR image into its several chemical shift components. In the exemplary case of protons, which will be used hereafter for illustration, it maybe desired to portray as separate images the water and fat components of the subject. One method of accomplishing this is to acquire two images S.sub.O, and S.sub.-1 with the fat and water components of the images in phase, and out of phase by .pi. radians, respectively (the "Dixon" technique). Adding and subtracting these images provides separate fat and water images. The phase shift between the fat and water components of the images may be controlled by timing the RF pulses of the NMR sequence so that the signal from the fat image evolves in phase with respect to the water by the proper angle of exactly .pi., before the NMR signal is acquired.
In the ideal case above, the frequency of the RF transmitter is adjusted to match the Larmor frequency of the water. If the polarizing magnetic field B.sub.O is uniform, this resonance condition is achieved through out the entire subject. Similarly, the out-of-phase condition (.pi. radians) for the fat component is achieved for all locations in the subject under homogeneous field conditions. In this case, the decomposition into the separate images is ideal in that fat is completely suppressed in the water image, and vice versa.
When the polarizing field is inhomogeneous, however, there are locations in the subject for which the water is not on resonance. In this case, the accuracy of the decomposition breaks down and the water and fat images contain admixtures of the two species. This derives from additional phase shifts of the NMR signal caused by the off resonance condition. The degree to which the off resonance condition holds is, in general, not known. The accuracy of such chemical shift "Dixon" techniques is therefore often unreliable.
Field inhomogeneities may result from improper adjustment or shimming of the polarizing magnetic field B.sub.O, but are more typically the result of "demagnetization" effects caused by the variations in magnetic susceptibility of the imaged tissue, such as between soft tissue and air, or bone and soft tissue, which locally distort the polarizing magnetic field B.sub.O. These demagnetization effects may be of short spatial extent but of high magnitude, and therefore may not be removed by conventional linear or higher order shimming techniques.
The influence of demagnetization may be accommodated, however, by an imaging technique that uses three images S.sub.O, S.sub.1, and S.sub.-1, with the phase evolution times adjusted so that the fat and water components of the images in phase, out of phase by .pi., and out of phase by -.pi. respectively. The complex pixels in each of the three images after conventional reconstruction may be represented as follows: EQU S.sub.O =(.rho..sub.1 +.rho..sub.2)e.sup.i.phi.O ( 2) EQU S.sub.1 =(.rho..sub.1 -.rho..sub.2)e.sup.1(.phi.+.phi.0) ( 3) EQU S.sub.-1 =(.rho..sub.1 -.rho..sub.2)e.sup.-i (.phi.-.phi.O) ( 4)
where .rho..sub.1 is the (real) relaxation weighted spin density and hence the amplitude of the pixel contributed by the water component, .rho..sub.2 is the (real) relaxation weighted spin density or amplitude of the pixel contributed by the fat component, and .phi..sub.0 is the phase shift common to all acquisitions that is caused by RF heterogeneity due to penetration effects, phase shifts between the RF transmitter and receiver, and other systematic components. These effects are independent of chemical shift but dependent on spatial location. In images S.sub.1 and S.sub.-1 the amplitudes .rho..sub.1 and .rho..sub.2 are subtracted because of the .pi. and -.pi. phases shift between the fat and water components as previously described. The phase shift .phi. is caused by the unknown resonance offset that results from B.sub.O heterogeneity. The phase offset .phi..sub.0 may be eliminated from equations (2)-(4) from S.sub.O, since the .rho..sub.i values are real quantities, by determining its argument .phi..sub.0. The argument .phi..sub.0 may then be eliminated from the equations (2)-(4) yielding: EQU S'.sub.O .ident.S.sub.O e.sup.-e.phi.0 =(.rho..sub.1 +.rho..sub.2) (2') EQU S'.sub.1 .ident.S.sub.1 e.sup.-i.phi.0 =(.rho..sub.1 -.rho..sub.2)e.sup.i(.phi.) ( 3') EQU S.sub.-1.sup.'.ident. S.sub.-1 e.sup.-i.phi.0 =(.rho..sub.1 -.rho..sub.2)e.sup.-i(.phi.) ( 4')
The values of .rho..sub.1 and .rho..sub.2 may be determined from the measured values of S.sub.O.sup.', S.sub.1.sup.' and S.sub.-1.sup.' according to equations (2')-(4') as: ##EQU1## where s is a "switch function" which may be either +1 or -1 thus determining the sign of the square root.
The choice of the sign of the square roots is difficult because the demagnetization effects may cause abrupt changes in the local polarizing magnetic field B.sub.O which cause the switch function to change in value from pixel to pixel.